将数学建模的思想融入高等数学的教学

1、将数学建模的思想融入高等数学的教学    将数学建模的思想融入高等数学的教学 【中文摘要】 随着我国高等院校大范围的扩大招生,学生的个体差异和数学基础的差别越来越大,而作为高等学校的重要基础课程的高等数学的教学改革也正在进行研究和探讨之中,许多教育同行都深深的感到,如今的高等数学教学不能还是同一个模式、同一个要求。在终身学习这种思想的指导下,高等数学的教育方式和教学模式也正在经历一次一次的变革。本文从高等学校中高职高专学生的学习特征和规律出发,以问题研究为手段,以全面掌握和熟练运用所学知识解决实际问题为目标,结合高等数学的学科特点,进行基于数学建模思想融

2、入高等数学的教学模式的研究分析与评价,并对教学效果进行分析与评价,促使教师改变教学模式,从而提高学生的课堂学习效率和学生数学素养,进而提高学生的整体综合素质。本文采用问卷调查、教学实践研究、建立马尔科夫教学评价模型分析等方法,结合高等数学教学大纲的要求,将数学建模的思想融入高等数学教学,并通过课堂教学的实践,使建模思想和数学理论有机的结合。将建模思想融入高等数学教学,为正在进行的高等学校教育教学改革提供了新的思路和方法,与此同时,本人根据教学改革的需要,对实施教学改革的班级和对照班进行了相应的教学效果分析和评价。本文共分六个章节,其主要内容如下:第一章:研究背景。通过对宏观背景的研究,提出问题

3、。第二章:建模思想融入高等数学教学模式的基本思路。结合我校实际提出建模思想融入高等数学的教学设计。第三章:建模思想融入高等数学的教学的教学案例。第四章:建模思想融入高等数学的教学实践。第五章:教学效果调查与评价。第六章:教学反思 【英文摘要】 As the institutions of higher education of our country expand the enrollment broadly, students' individual differences and the differences on mathematics foundation are great

4、er and greater. The reform in education of“higher mathematics”is carrying on research and discussion, which is the important basic course of the institution of higher education. A lot of college teachers consider that teaching of“higher mathematics”of today can't be still in the same mode and th

5、e same requirement. Under the guidance of this kind of thought studying all the life, the education way and teaching mode of“higher mathematics”are changing again and again. The author of this paper proceeds from study characteristic and law of the students of the high commissioner of the professors

6、hip in the institution of higher education, regards studying problems as the means, regards grasping the goal in an all-round way and using it to solve the practical problem, combines the discipline characteristic of“higher mathematics”, carries on researching and analyzing and appraisal of the teac

7、hing mode based on that the modeling thought of mathematics incorporates higher mathematics, and analyzes and appraises the teaching result, thereby impelling teachers to change the teaching mode, thus improving students' classroom learning efficiency and student's mathematics accomplishment

8、, and then improving students' whole overall qualities.The author of this paper takes the methods of analyzing that appraising models by questionnaire investigation, teaching practice, the establishment of teaching evaluation Markov model analysis, combines the requirement for“higher mathematics

9、”syllabus, integrates the idea of mathematical modeling into the higher mathematics teaching. And through practice of classroom teaching, combines modeling thought with mathematics theory. It has offered new thinking and method for ongoing reform in education of higher school education that incorpor

10、ating teaching of“higher mathematics”of the modeling thought. Meanwhile, according to the needs of reform in education, the author contrasts the class and analyzes the corresponding teaching result to the class. This paper divides into six chapters, its main content is as follows:Chapter: Study of t

11、he background. Through the study of macroscopically background put forward the question.Chapter: The modeling thought incorporates the basic thinking of the teaching mode of“higher mathematics”. The author made light of the actual modeling school thinking into the design of higher mathematics teachi

12、ng. Chapter: The modeling thought incorporates the teaching of higher mathematics to teaching cases.Chapter: The modeling thought incorporates the teaching of higher mathematics to practice.Chapter: The teaching result is investigated and appraised.Chapter: Teaching reviews. 【中文关键词】 高等数学; 建模思想; 基本思路

13、; 教学设计; 教学实践 【英文关键词】 Advanced Mathematics; The idea of mathematical modeling; Basic thinking; Instructional design; Teaching practice 【毕业论文目录】中文摘要 4-5 Abstract 5-6 第一章 问题的提出 10-19     1 研究背景 10-11         1.1 高等数学课程发展的历史沿革 10     

14、    1.2 国内外利用数学建模教学的背景与状况分析 10-11     2 高等数学的教学目标 11-13         2.1 高等数学的总体目标 11         2.2 我校（河北北方学院）高等数学课程的教学目标 11-13     3 在我校高职高专高等数学教学中融入建模思想的必要性与可行性 13-15     

15、;    3.1 建模思想融入高等数学教学的必要性 13-14         3.2 建模思想融入高等数学教学的可行性 14-15     4 相关研究综述与现状 15-19         4.1 对数学建模理论的研究 15-17         4.2 将数学建模思想融入数学主干课程的研究 17-19 第二章 将建模思想融

16、入高等数学教学的基本思路 19-32     1 实验目的与研究的问题 19-20     2 数学建模融入到高等数学教学中的方法 20-21         2.1 弄清、搞透概念的意义 20         2.2 加深、推广应用问题 20-21         2.3 高等数学中数学模型的案例教学 21  

17、60;  3 在高等数学中要全方位渗透数学思想方法 21     4 针对我校高等数学融入建模思想的教学设计 21-31         4.1 设计思想 21-22         4.2 教学设计的实施 22-31     5 教学实践 31     6 教学反思 31-32 第三章 在高等数学教学中融入数学建模思想的案例 32-47  

18、60;  1 建模思想在概念、定义教学中的融入 32-38         1.1 导数概念的引入 32-35         1.2 定积分定义的教学 35-38     2 建模思想在定理应用教学中的融入 38-41         2.1 连续函数的根的存在定理 38-39      

19、0;  2.2 建模思想融入极大极小化问题 39-41     3 运用建模思想分析解决实际应用问题 41-47         3.1 贷款购房函数的应用 41-42         3.2 投资费用问题级数的应用 42-45         3.3 电学问题微分方程的应用 45-47 第四章 建模思想融入高等数学的教学实践 47-52 

20、0;   1 教学实践的实验设计 47-49         1.1 实验目的与假设 47         1.2 实验对象的选取 47         1.3 实验方法 47         1.4 干扰变量控制 47         1.5 实验内容分析分期付款模型 47-49     2 在数学教学中融入建模思想的主要困难和策略 49-52